Cambridge IGCSE Mathematics - International 0607 — 2012 May/June Paper 2 · Variant 2

This document consists of 8 printed pages. IB12 06_0607_22/5RP © UCLES 2012 [Turn over *0334232765* For Examiner's Use UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended) May/June 2012 45 minutes Candidates answer on the Question Paper Additional Materials: Geometrical Instruments READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. CALCULATORS MUST NOT BE USED IN THIS PAPER. All answers should be given in their simplest form. You must show all the relevant working to gain full marks and you will be given marks for correct methods even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40. www.XtremePapers.com

2 © UCLES 2012 0607/22/M/J/12 Formula List For the equation ax2 + bx + c = 0 x = 2 _ ± 4 2 _ b b ac a Curved surface area, A, of cylinder of radius r, height h. A = 2πrh Curved surface area, A, of cone of radius r, sloping edge l. A = πrl Curved surface area, A, of sphere of radius r. A = 4πr2 Volume, V, of pyramid, base area A, height h. V= 1 3 Ah Volume, V, of cylinder of radius r, height h. V = πr2h Volume, V, of cone of radius r, height h. V = 1 3 πr2h Volume, V, of sphere of radius r. V = 4 3 πr3 = = sin sin sin a b c A B C a2 = b2 + c2 – 2bc cos A Area = 1 2 bc sin A A a B C b c

3 © UCLES 2012 0607/22/M/J/12 [Turn over For Examiner's Use Answer all the questions. 1 (a) Find the value of 2 1 49 − . Answer(a) [1] (b) When 4 2 = − x write down the values of x. Answer(b) x = or x = [2] 2 (a) Factorise 2 6 2 − −x x . Answer(a) [2] (b) Solve the equation 0 2 6 2 = − −x x . Answer(b) x = or x = [1]

4 © UCLES 2012 0607/22/M/J/12 For Examiner's Use 3 p =       3 2 q =      − 5 3 Find (a) 2p – 3q, Answer(a)         [2] (b) p . Answer(b) [2] 4 Find the next two terms in this sequence. 1, 2, 6, 15, 31, … Answer , [2]

5 © UCLES 2012 0607/22/M/J/12 [Turn over For Examiner's Use 5 Factorise completely. (a) qx xy py pq − + − Answer(a) [2] (b) 2 2 50 32 d c − Answer(b) [2] 6 (a) For the function x y 2 sin 3 = write down (i) the amplitude, Answer(a)(i) [1] (ii) the period. Answer(a)(ii) [1] (b) Sketch the graph of x y 2 sin 3 = on the axes below for o 0 Y x Y o 360 . y x 4 0 –4 90° 180° 270° 360° [2]

6 © UCLES 2012 0607/22/M/J/12 For Examiner's Use 7 Solve the simultaneous equations. 3p + 4q = 7 5p + 6q = 10 Answer p = q = [4] 8 y varies directly as 2 x , where x is a positive integer. When x = 3, y = 108. Calculate the value of x when y = 300. Answer x = [3]

7 © UCLES 2012 0607/22/M/J/12 [Turn over For Examiner's Use 9 Joe is training for a triathlon. During one training session he • swims 1 km in 15 minutes, • cycles 20 km at a speed of 20 km/h, • runs at a speed of 8 km/h for 45 minutes. Calculate Joe’s average speed for the training session. Give your answer in kilometres per hour. Answer km/h [3] 10 Solve the equation. 1 14 1) 3( 7 3 = − − + x x Answer x = [3] Questions 11 and 12 are on the next page.

8 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. © UCLES 2012 0607/22/M/J/12 For Examiner's Use 11 (a) Write as a single logarithm. 2 log 4 log 3 log − + Answer(a) [1] (b) Make x the subject of x y 3 log = . Answer(b) x = [1] (c) Simplify completely. 3 27 Answer(c) [1] 12 The co-ordinates of three points are A(−2, 6), B(6, 2) and C(−2, −2). (a) Find the gradient of AB. Answer(a) [1] (b) D is the midpoint of AB. By using gradients show that the straight lines AB and CD are not perpendicular. [3]

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/22 Paper 2 (Extended), maximum raw mark 40 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. • Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the May/June 2012 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses. www.XtremePapers.com

Page 2 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 22 © University of Cambridge International Examinations 2012 1 (a) (b) 7 1 ) (± (0.1528…) 2 1 ± (± 0.5) 1 2 Accept 7 1 − (–0.1528...) M1 for x2 = 4 1 soi [3] 2 (a) (3x − 2 )(2x + 1) 2 SC1 for a pair of brackets which multiply out to give 2 terms correct (b) 3 2 , 2 1 − 1ft ft from their (a) only if SC1 scored in (a). Strict ft but can start again to achieve correct answer and score. [3] 3 (a)       −9 13 2 B1 for       k 13 or       −9 k seen (b) 13 isw 2 B1 for 22 + 32 seen or implied by 13 ± [4] 4 56, 92 2 B1 for 56, B1 for 92 After B0, B0, award SC1 for 25 and 36 seen. [2] 5 (a) (b) (q – y)(p – x) oe 2(4c – 5d)(4c + 5d) 2 2 B1 for p(q – y) + x(y − q) or better, or q(p – x) + y(x – p) or better B1 for 2(16c2 – 25d2) or (8c – 10d)(4c + 5d) or (4c – 5d)(8c + 10d) [4] 6 (a) (i) (ii) 3 180° or π 1 1 (b) y = 3sin2x drawn B2 After B0, SC1 for any wave with correct amplitude or their amplitude and SC1 for wave passing through (0,0) with correct period or their period [4] 7 p = −1, q = 2.5 or 5/2 4 M1 for attempt to get 2 equations for elimination. Condone 1 numerical slip M1 for correct addition/subtraction of their equation. Condone 1 further numerical slip (dep) A1, A1 for each Or M1 for equation in form x = or y =. Condone 1 numerical slip M1 for substitution of their equation into the other correctly. No further slip A1, A1 for each Or wwwSC3 for either p = –1 or q = 2.5 [4] 8 x = 5 3 M2 for y = 12x2 or 2 2 3 300 108 x = oe M1 for y = kx2 (k ≠ 1) [3]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper IGCSE – May/June 2012 0607 22 © University of Cambridge International Examinations 2012 9 13.5 3 B1 for total distance = 27km B1 for total time = 2 hours [3] 10 x = −5 3 M1 for multiplying all 3 terms by 14, or LHS over 14 = 1, or all over 14 A1 for 2(x + 3) – 3(x – 1) = 14, or 14 )1 ( 3 6 2 − − + x x = 1 oe with other denominator e.g. 98 –5 may be seen embedded [3] 11 (a) log 6 1 (b) 3y 1 (c) 3 1 Accept ±3 or –3 [3] 12 (a) (b) 2 1 − oe For co-ordinates of D = (2, 4) For gradient of CD = 4 6 oe e.g. (‘4’ – –2)/(‘2’ – –2) Gradients not negative reciprocals oe 1 M1 M1 E1 isw (incorrect cancelling only) Can imply previous M1 i.e. Correct method using their D Dep on M2 and no errors in (b) [4]